Information Manifold Model – Volume II: Entropy, Curvature, and Constraint Across Physical 0Systems

The Information Manifold Model (IMM) treats complex systems as structured information spaces whose observable dynamics emerge from entropy gradients, geometric constraint, and boundary conditions rather than prediction or optimization. Volume II develops the model by framing system evolution as motion across curved information manifolds. Drawing conceptual structure from quantum mechanics, thermodynamics, and general relativity, this volume explores how uncertainty, entropy, and constraint shape state transitions in both physical and market systems. Rather than proposing a unification of physics domains, this work identifies shared structural principles: information curvature, invariant constraints, entropy-driven evolution, and persistence across state-space. Market behavior is examined as one instantiation of these principles, where price movement reflects the resolution of informational tension under constraint. Key contributions include: Formalization of information manifolds as constrained state-spaces Entropy as a directional structural force rather than a statistical artifact Curvature-based interpretation of state transitions Conceptual alignment between market dynamics and physical systems A non-predictive framework grounded in structure rather than optimization This volume is exploratory and foundational. Its purpose is to establish a rigorous conceptual scaffold for later formalization, simulation, and domain-specific instantiations.